Let PQ be a focal chord of the parabola `y^(2)=4ax`. The tangents to the parabola at P and Q meet at point lying on the line
`y=2x+a,alt0`.
If chord PQ subtends an angle `theta` at the vertex of `y^(2)=4ax`, then `tantheta=`

Options

A. `2sqrt(7)//3`
B. `-2sqrt(7)//3`
C. `2sqrt(5)//3`
D. `-2sqrt(5)//3`

Answer

D

Explanation

4 Angle made by chord PQ at vertex (0,0) is given by
`tantheta|(m_(OP)-m_(OQ))/(1+m_(OP)*m_(OQ))|((2//t)+2t)/(1-4)=(2{(1//t)+t})/(-3)=(-2sqrt(5))/(3)`